Jefferson was visionary and crafty. In Hamilton, he met his match. How the rivalry lives on.

On March 21, 1790, Thomas Jefferson belatedly arrived in New York City to assume his duties as the first Secretary of State after a five-year ministerial stint in Paris. Tall and lanky, with a freckled complexion and auburn hair, Jefferson, 46, was taken aback by the adulation being heaped upon the new Treasury Secretary, Alexander Hamilton, who had streaked to prominence in his absence. Few people knew that Jefferson had authored the Declaration of Independence, which had yet to become holy writ for Americans. Instead, the Virginian was eclipsed by the 35-year-old wunderkind from the Caribbean, who was a lowly artillery...